If your antenna is motionless, then a receive antenna oriented in the same plane is most efficient. A spiral antenna is used to receive a circularly polarized signal. Receive antenna efficiency is determined by how resonant the structure is with the RF energy it has been designed to receive.

Efficiency in transmitting (not "broadcasting") mostly has to do with how closely the antenna impedance matches the transmitter impedance.

There are a lot of types of antenna's. On this page there are links to pages with antenna's.http://www.educypedia.be/electronics/antennatypes.htm
Some are better for transmitting and others are better for recieving.
For transmitting the matching of the transmitter and the antenna is very important, you want to have all the power to go to the antenna.

I think a coiled antenna can be made smaller than a straight antenna, because the coil acts like an inductor in series with the antenna. This causes the antenna to be tuned to a lower frequency than a straight antenna of the same length.

Antennas are a science unto themselves. They are for some of us, a most interesting subject. A google search for "antenna design basics" will yield many useful links.
Here is also a good place to start: http://www.ac6v.com/antprojects.htm#theory

Generally a full size 1/4 wave whip will work better than a "loaded" 1/4 whip.... one made shorter by helically winding and tuning a length of wire on a fibreglass whip.
They will both tune the same frequency, and the transmitter will see little difference, but by virtue of a reduced "Capture" area, the helical will not perform as well. It will also have a narrower Bandwidth.